Is there an intuitive proof of $\sin(x + y)= \sin x\cos y+ \sin y\cos x$ when $x + y > 90^\circ$?

I saw nice geometric proof of $\sin{(x + y)} = \sin{x}\cos{y} + \sin{y}\cos{x}$ using unit circle. But I can't find proof when $x + y > 90^\circ.$

Is there intuitive, "simple" or geometric way to prove this? Can we maybe transform unit circle or what is going on here?